Question

Assertion : If distance between the parallel plates of a capacitor is halved, then its capacitance is doubled
Reason: The capacitance depends on the introduced dielectric

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (B)

The capacitance of a parallel plates capacitor is given by $C=\frac{{\epsilon }_{0}A}{d}$
where $A$ is area of each plate, $d$ is the distance between plates
$\therefore \frac{C_1}{C_2}=\frac{\frac{{\epsilon }_{0}A}{d}}{\frac{{\epsilon }_{0}A}{d/2}}=\frac{1}{2}\therefore C_2=2C_1$
When dielectric of dielectric constant $k$ is introduced in between the plates then the capacitance $C=\frac{k{\epsilon }_{0}A}{d}$ i.e. $C\propto K$
Capacitance $C$ depends on introduced dielectric